Var Calculation

Statistical Variance Calculator

Sample Variance (n-1) Population Variance (n)

Calculation Results

Count (n) 0

Mean (μ or x̄) 0

Variance (σ² or s²) 0

Std. Deviation (σ or s) 0

Sum of Squares: 0

Understanding Statistical Variance

Variance is a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average) and thus from every other number in the set. Variance is often depicted by this symbol: σ².

How to Calculate Variance Manually

To find the variance, follow these essential steps:

1. Find the mean: Add up all the numbers in your data set and divide by the count of numbers.
2. Subtract the mean from each number: This gives you the deviation from the mean for each data point.
3. Square each result: This ensures all values are positive.
4. Sum the squares: Add all the squared results together (Sum of Squares).
5. Divide: For Population Variance, divide by the total count (n). For Sample Variance, divide by the count minus one (n-1).

Sample vs. Population Variance

The choice between sample and population variance depends on whether you are analyzing every single member of a group (Population) or just a representative subset (Sample).

• Population Variance: Used when you have data for every member of the group you are studying (e.g., test scores for every student in a single small classroom).
• Sample Variance: Used when the data is a random selection from a larger group (e.g., surveying 100 voters to represent an entire city). Using n-1 (Bessel's correction) helps provide an unbiased estimate of the population variance.

Example Calculation

Imagine you have a data set: 5, 10, 15.

1. Mean = (5 + 10 + 15) / 3 = 10.
2. Squared differences: (5-10)² = 25; (10-10)² = 0; (15-10)² = 25.
3. Sum of squares = 25 + 0 + 25 = 50.
4. Sample Variance = 50 / (3 – 1) = 25.
5. Population Variance = 50 / 3 = 16.67.

function calculateVariance() { var rawData = document.getElementById("dataset").value; var type = document.getElementById("calcType").value; var errorDiv = document.getElementById("error-message"); var resultsDiv = document.getElementById("results-area"); errorDiv.style.display = "none"; resultsDiv.style.display = "none"; // Clean data: replace commas and newlines with spaces, then split var cleanData = rawData.replace(/[,;|\n]/g, ' '); var parts = cleanData.split(/\s+/); var numbers = []; for (var i = 0; i < parts.length; i++) { var num = parseFloat(parts[i]); if (!isNaN(num)) { numbers.push(num); } } if (numbers.length < 2) { errorDiv.innerHTML = "Please enter at least 2 valid numbers to calculate variance."; errorDiv.style.display = "block"; return; } // Calculate Mean var sum = 0; for (var j = 0; j < numbers.length; j++) { sum += numbers[j]; } var mean = sum / numbers.length; // Calculate Sum of Squares var sumOfSquares = 0; for (var k = 0; k < numbers.length; k++) { sumOfSquares += Math.pow(numbers[k] – mean, 2); } // Calculate Variance var divisor = (type === "sample") ? (numbers.length – 1) : numbers.length; var variance = sumOfSquares / divisor; var stdDev = Math.sqrt(variance); // Display Results document.getElementById("res-count").innerText = numbers.length; document.getElementById("res-mean").innerText = mean.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4}); document.getElementById("res-variance").innerText = variance.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4}); document.getElementById("res-stddev").innerText = stdDev.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4}); document.getElementById("res-ss").innerText = sumOfSquares.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4}); resultsDiv.style.display = "block"; }